"AMCU believes that this failure will jeopardise the health of a quarter million mineworkers, as well as their host communities," it said, requesting the matter be heard urgently.
Most mines were shuttered as the country entered a 21-day lockdown in March but Mantashe said last week mines could now operate at 50% capacity after the lockdown was extended to April 30.
The AMCU said authorities had not exercised their powers to impose binding regulations on employers, to protect mineworkers from the pandemic.
It said the provisions currently in place "fell short" and mining companies had responded differently to implementing risk mitigation measures.
In the papers submitted to the court, the AMCU included expert opinions from leading health figures who said a binding, national standard was required.
The AMCU also said the unlocking of mines had caused "utter confusion".
It referred to the charges laid against Impala Platinum for recalling workers last week, allegedly in contravention of regulations, and included a letter from the police union to the police minister asking for "clear directives on the permissions they [miners] are alleging they have to operate".
The AMCU said it was not opposing or trying to obstruct the return to work for the mining sector but wanted to protect members' rights to health and safety.
The union has named Mantashe, the chief inspector of mining, the Minerals Council of South Africa and the minister of cooperative governance and traditional affairs as respondents, and said the first three had given notice of their intent to oppose the application.
The AMCU tweeted a short while ago the Labour Court had granted an order setting down its application to April 29.
The union had brought another application against the mines department, asking the High Court to set aside the minister's decision to exempt 129 mines from COVID-19 regulations for being essential mining services.
However, it said the issue had become less urgent since the amendments allowing mines to ramp up, and it would formally remove the matter from the urgent role "to be argued later during the normal course".